The present invention relates in general to web forming processes and, more particularly, to improved cross-machine direction control of such processes. While the present invention can be applied to a variety of systems, it will be described herein with reference to a web-forming machine used for making sheets of paper for which it is particularly applicable and initially being utilized.
Uniformity of a property of a web of sheet material can be specified as variations in two perpendicular directions: the machine direction (MD), which is in the direction of web movement during production, and the cross-machine direction (CD), which is perpendicular to the MD or across the web during production. Different sets of actuators are used to control the variations in each direction. CD variations appear in measurements known as CD profiles and are typically controlled by an array of actuators located side-by-side across the web width. For example, in a paper making machine, an array of slice screws on a headbox or an array of white-water dilution valves distributed across a headbox are usually used to control the weight profiles of webs of paper produced by the machine.
Control schemes are used to control the CD actuators in order to reduce the variations at different CD locations across the web. For such schemes to succeed, it is crucial to apply control adjustments to the correct actuators, i.e., actuators that control areas of the web in which CD variations are to be reduced. Hence, the spatial relationship between the CD location of an actuator and the area of the profile the actuator influences is key to the implementation of a high-performance CD controller. The cross direction spatial relationship, between CD actuators and a CD profile, is known to those skilled in the art as “CD mapping”. FIG. 1 shows an example of a CD mapping relationship 100 wherein bumps 102 made to actuators in an actuator array are reflected in the CD profile 106.
In many sheet-forming processes, the CD mapping relationship is not a linear function. For example, on a paper-making machine, the CD mapping between the headbox slice screws or dilution valves and weight profile is particularly non-linear near the edges of the web due to higher edge shrinkage. The nonlinear mapping relationship is a function of various machine conditions. The relationship cannot be easily represented with a fixed explicit function. Particularly in an ongoing web making operation where the CD mapping can change either gradually or abruptly, depending on the evolution of machine conditions.
Misalignment in the CD mapping can lead to deterioration in control performance. One typical symptom of mapping misalignment is the presence of sinusoidal variation patterns in both the CD profile and the actuator profile. The appearance of the sinusoidal pattern is often referred to in the art as a “picket fence” pattern or “pickets.” The picket fence cycles that appear in both the CD profile and the actuator profile occur in the same region of the sheet and are usually of comparable spatial frequencies. Another typical symptom of mapping misalignment is the presence of sinusoidal variation patterns in the MD lanes corresponding to the sinusoidal variation patterns developed in both the CD profile and the actuator profile. The appearance of the sinusoidal pattern in the MD lanes in combination with the “picket fence” pattern is often referred to in the art as a “walking pattern”. The patterns are caused by the control actions being applied to the misaligned actuators.
Although the mapping misalignment can be corrected by adjusting the control setup, often such adjustment has required manual intervention. Dependent on the frequency of CD mapping changes, the number of manual interventions may be significant. At a minimum, manual intervention requires determination of how wide the sheet is at the forming end (location of the process where the actuator array is situated) and at the finishing end (location of the process where the CD profiles are measured). While these determinations may be sufficient to satisfy processes with very minimal nonlinear shrinkage, for processes with greater non-linear shrinkage, the scope of manual intervention may require perturbing the actuator array, at multiple locations, to determine the mapping relationship between the actuators and the CD profile. Such perturbations or “bumps” are typically performed with the CD control system turned off. Additionally, only a few actuators, spaced sufficiently far apart, are normally perturbed at a given time to ensure separation of the response locations in the CD profile. For a CD control system with a large actuator array, such perturbations or bumps may consume an extended period of production on the process.
Automated on-line mapping misalignment correction has been proposed based on using global indicators, such as variability of the entire CD profile, to identify a plurality of misalignment problems across the web and to activate corresponding profile optimization sequences. See, for example, U.S. patent application Ser. No. 09/592,921, entitled AUTOMATED OPTIMIZATION OF CROSS MACHINE DIRECTION PROFILE CONTROL PERFORMANCE FOR SHEET MAKING PROCESSES, that was filed Jun. 13, 2000, is assigned to the same assignee as the present application, is incorporated herein by reference and is now U.S. Pat. No. 6,564,117. Unfortunately, if global indicators are used, local profile problem areas have to get to product damaging levels before corrective action can be taken and, since a plurality of problems are identified at a given time, problems that do not occur at that time are not addressed.
In addition, such correction schemes have assumed that the performance curve can be classified as a curve with a sharply defined minimum, such as a “V” shape. This form of performance curve has an optimal solution at the sharply defined minimum point. The inventors of the present application have determined that is not the case but rather, in cross direction applications, the performance curve is characterized by sharp edges and a wide, flat central region “\______/” such that the optimal point is near the center of the flat region and not near the sharply defined edges. Accordingly, previously proposed misalignment correction schemes find an optimal point at the sharply defined edges, which are points that are marginally stable. Further, a persistent “bad” spot in the profile resulting from mechanical problems can be identified as having a profile problem that needs to be probed resulting in time searching for a solution to a problem that cannot be solved.
It is also possible to control the smoothness of the setpoints of the actuator array, i.e., to restrict the setpoint differences between adjacent actuators in the actuator array, to reduce the amplitude of the cycles. Control of smoothness is also a mechanism for making the CD control system more robust for modeling uncertainty under different process conditions and the presence of uncontrollable variations in the CD profile.
Accordingly, there is an ongoing need in the art for improved cross-machine direction (CD) mapping control in web making machines that can overcome changes in the mapping relationships between CD actuators and the corresponding CD profile of the web that they control. The control arrangement would correct the mappings without interruption of the CD control system and preferably would also control the smoothness of the setpoints of the actuator array instead of or in addition to corrections of the mappings.